Tom Chivers is the Telegraph's assistant comment editor. He writes mainly on science. Not a poet - that's the other Tom Chivers. Read older posts by Tom here.

Why is it taking so long to find MH370?

I was asked this by someone today, who obviously assumed that, because I'm a bit of a geek, I have some sort of insight into aircraft engineering and air-sea rescue search patterns. But I thought I'd have a go at answering it. The answer, by the way, is: because the ocean is big and planes are small. I've decided to be really nerdy about this, and explain just how big oceans are, and just how small planes are, with (roughly GCSE-level) MATHS: but if you're not in the mood for maths, that's the long and the short of it. The ocean: really big. Planes: pretty small.

Please do check my maths, by the way, and point out any mistakes.

Anyway. To give you an idea of how big the ocean is, you may remember, last year, a widely publicised story about a ghost ship full of cannibal rats which was heading for Britain.

Obviously there were no cannibal rats and everyone was being a bit ridiculous. But there was a ghost ship, an old Russian liner called the Lyubov Orlova, which had been lost while being towed from Newfoundland, Canada, to the Dominican Republic, where it was going to be scrapped.

The ship was lost in the west Atlantic, and the prevailing currents mean that it would have drifted east, vaguely towards Britain and Ireland. As Richard Fisher explained in a thoughtful piece about the Orlova in New Scientist, it's normally pretty easy to find a ship: they have transponders which give their position at all times. But the Orlova had been decommissioned and its transponder had long since been out of action.

Still, you might think, ships are pretty big. The Orlova weighed thousands of tonnes and was over a hundred metres long. And the place where it was lost, and its likely direction, were known. What's more, it was pretty tall; the top of its superstructure was about 15 to 20m above the horizon, judging by photos. Something 15 metres high can be seen above the horizon by someone at sea level from about 13.7 kilometres away. How you know this is simple geometry: visible distance = √(2 x radius of the Earth x height of the object).

(Side note: interestingly, if you didn't know the size of the Earth, you could work it out by how far ships travelled before you couldn't see them any more. If you know a 20m-tall ship gets 15km away before its mast drops below the horizon, you can simply rearrange the equation. So radius of the earth in metres = (13,700^2) ÷ (15 x 2) = 6,256,333. It's actually 6,378,333m, but close enough, since I was rounding off. That's not how the ancient Greeks did it, as it happens – Eratosthenes used a stick, a shadow and a well – but they could have done.)

The Orlova, then, could have been seen from anywhere up to 13.7km away (NOTE: as someone's pointed out in the comments, this is by someone with their eyes literally at sea level, because I was lazy about doing more maths. To work out how far away you could see the Orlova from if you're higher than that, which obviously you would be, do the same sum for your height and add the result to that 13.7km). You'd think it'd be quite hard to lose something when you can see it from a distance of eight and a half miles. But it's not, it's really pretty easy.

A circle with a radius of 13.7km – the circle from within which the Orlova could, in theory, be seen on a clear day – would have an area of 589 square kilometres. (Area of circle = π times the square of the radius.) That's quite a big area. But the area of the Atlantic Ocean, according to the US National Oceanic and Atmospheric Administration, is 106,460,000 square kilometres.

If you were dropped somewhere at random in the Atlantic Ocean, your odds of landing in sight of the Orlova would be 589 in 106,460,000, or about 0.0006 per cent. The Atlantic Ocean is massive. (The Pacific Ocean, by the way, is about twice as big.) Assuming the Orlova was stationary, you'd have to take about 120,000 such random samples before your odds of finding the ship reached 50 per cent. And that's before we take into account things like variable visibility, choppy seas, and the fact that not every single microscopic blob winking momentarily above the horizon will be noticed and examined. Oh, and night time.

What night time might look like. (Artist's impression.)

The Orlova was never found. It probably sank, although Fisher points out that only two of its six lifeboats triggered their radio beacons, which has led searchers to think that it might still be out there. He also mentions that a Swedish steamer called the Baychimo, abandoned in pack ice in 1931, was spotted at various points up and down the Alaskan coast until 1969 (and not at all since). Ships can survive a long time without either being seen or sinking.

The MH370, though, was not a ship, and after it crashed into the sea it would have sunk pretty quickly. So the option of spotting it on the horizon is not there. There was a lengthy search for debris and oil slicks, but it was always a long shot, for the reasons I've just outlined regarding the Orlova.

If it were the case that MH370 was simply lost on the sea bed somewhere within its fuel range and no one knew where, it would be a statistical impossibility to find it. But there are more sophisticated statistical ways of doing it, Bayesian analysis which can narrow down search patterns to the most likely areas; this episode of BBC Radio 4's More or Less programme has a very interesting rundown of how those techniques, first developed to look for U-boats in the Second World War, helped to find the missing Air France jet AF447 in 2011, two years after it crashed.

Those techniques may have helped, because several "pings" have been heard by sonar on search ships. They aren't pings, really, in the sense that fans of Das Boot and The Hunt for Red October might imagine: they're ultrasonic, over 33,000Hz (cycles a second); human ears can only hear up to about 20,000Hz. Those pings are believed to have been given off by the MH370's black box, in an automated response to being submerged in water following a crash. And according to the Australian government, they limit the area the black box is in to a mere 41,393 sq km. That's a circle of about 115km radius, pi fans.

It appears, by the way, to be a minor miracle that the pings were heard at all, if indeed they have. While we hear stories about whale-song travelling across whole oceans, high frequency sound doesn't travel all that far in water; the black box pinger's range is about 6,100m. The depth of the ocean where the wreckage has been found is about 4,500m, so even at the extreme range, the pinger would only be detectable in a circle a few kilometres wide on the surface. And sound behaves very oddly underwater; it can reflect off or be distorted by differences in temperature or pressure or salinity, not to mention simply being drowned out by other noises and wave action. And the battery on the pinger was expected to last about 30 days; it's apparently dead now, but it made it well past that date. If the pings have been detected, the searchers have got very lucky indeed already.

But it seems they have. Now, if we could send an underwater robot which can see as far along the sea bed as our imaginary Orlova-hunter could see along the surface, that'd be pretty much search over; just send the thing on a systematic pattern throughout the search area, and it would find the wreckage in a few hours, or maybe days. But that's not the case.

Now that the pings have been detected, the search is being carried out using an unmanned submarine called the Bluefin 21. It "flies" at 30m above the sea bed and uses side-scanning sonar to cover an area 500m either side of it. But it only moves at about 3 knots, 5.5km/h, so it would cover about 5.5 sq km an hour. 41,393 ÷ 5.5 = 7,526 hours. In perfect operating conditions, the Bluefin would take 314 days of constant searching to search the area completely.

But the Bluefin is in fact only searching an area of about 600 sq km, near where the Australian ship ADV Ocean Shield first heard the suspected pings. If that happens to be where the MH370 is, then it would take the sub a mere 100 hours or so of constant searching to cover it completely, in perfect conditions.

But conditions aren't perfect. For one thing, the Bluefin has a maximum operating depth of 4,500m; the water in the area is around that depth and sometimes deeper, so it has already had to abort its mission once after accidentally going too deep. And for another, it's not operating over a smooth flat surface; the bottom of the Indian Ocean is home to various huge underwater mountain ranges. It looks like the MH370 search area is a good distance away from the edges of the tectonic plates, so it may be a smoother area, but it is still a technically difficult search at the very edge of the submarine's operating abilities. The search teams are already considering giving up on the Bluefin and using a specialised deepwater remote operated vehicle.

The answer, then, to the question "why is it taking so long to find MH370?" is: because oceans are big and planes are small. The one thing we can add, at this stage, is that oceans are also really, really deep (really, really, really deep), and the devices we have to search through them are small and slow. If the MH370 wreckage is in the Ocean Shield search area, it may well be found soon. If it's in the larger one, it will be far harder.